A practicable formulation for the strength of glass and its special application to large plates

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A practicable formulation for the strength of glass and its special

application to large plates

Brown, William C.

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https://nrc-publications.canada.ca/eng/view/object/?id=e877f8b7-caed-4570-b2d0-59461bc59291 https://publications-cnrc.canada.ca/fra/voir/objet/?id=e877f8b7-caed-4570-b2d0-59461bc59291

by

•

!

*A PRACTICABLE ｾｏｉｄＱｕｌａｔｉｏｎ＠ FOR THE STRENGTH OF GLASS AND ITS SPECIAL APPLICATION TO LARGE PLATES

by

W. G. Brown

(2nd draft , August 1970)

*This is an original research work , and when utilized should be referenced as :

Publication No . NRC 14372 Novembe r, 1974

•

d failure including

A

simplified description of delaye

ｾｾｭｰ･ｲ｡ｴｵｲ･＠

and relative

ｨｾｩ､ｾｴｹ＠

effects

was

incorporated

time,

into appropriate mathematical statistics to yield a generalized

failure probability relationship for glass.

Practicability was

demonstrated by correlating test results for large areas of

soda-lime plate glass from independent manufacture sources.

(The test results demonstrate a range of load-bearing capacity

of about 2:1 as a result of loading duration differences of

30:1 and surface area differences of

9·.1).

To supplement the

description of delayed

ｦｾｩｬｵｲ･＠

' two additional statis tic al

parameters describing the strength of this kind of glass we r e

established with the help of a separate stress-distribution

investigation.

Several

examp es were worked to show application

1

:

ｾ＠ ...

INTRODUCTION

THEORETICAL

Delayed failure of glass in the presence of water vapour

Experimenta.l verification

Appropriate mathematical statistics for glass Application to rectangular plates

CORRELATION OF TESTS ON PLATES Available experimental data

Deflections in simply-supported square plates Evaluation of experimental results

Correlation procedure

Implications of the correlation

Strength characteristics of large areas of soda-lime plate glass

ｅｸ｡ｭｊ＾ｬ･ｾ＠

DISCUSSIO N

REFERENCES

APPENDICES

I - One-dimensional stress equivalent of a two-dimensional stress Page 1 4 4 8 12 13 16 16 17 19 21 23 26 \ 27 30 32

a-1

II - Approximations

I II - Ta ble VI

I V

Determina t ion of

ｐ｡ｲ｡ｭ･ｴ･ ｾ＠

k .

Pa ge

b - 1 c- 1 d- 1 \

attention to the weakening effect of . pre - existing surface flaw s or scratche s in glass. As a result of the st r ess raising e ffect of these fla ws, "the measured failure strength of glas s in tension is usually several orders of magnitude lower than its theor e tical s tr e n gth . That this effect is real is borne out by the r esults of many tests since Griffith's time which show that ave ra ge measured strengths and frequency distributions are altered by d elibe r a te surface conditioning; for example, sand blas tin g , grinding, polishing, or e tchin g . Surface roughenin g results in reduced av e rage str e ngth and reduced variabilit y , wh e rea s smoothing op e r a tions r es ult in increased strength with att e ndant incre ased variability. It h as been aptly pointed out that th e ob s erved strength is not a pr operty of the g lass materials; it is, rather, a derived funct ion of both glass properties and flaw geometry.

Measured str eng th, however, is not sol ely dependent on surface treatment; the average meas ured failure stress in mois t air at room temperature is noted to de crease with increased duration of loading. This important phenomenon of delayed failure as dependent on atmospheric moisture cont e nt and tem-perature has been investigated in considerable detail,

particularly during the past decade. It is now generally accepted that slow flaw gro wth takes place as a result of stress ﾷ ｾｯｲｲｯｳｩｯｮ＠ combined with plastic-v i scous flow .

The pre se nt work ha d modest beginnin g s in that it was intended to improve upon th e empiricism of windo w desi g n . It became apparent , however, that while extensive engineering tests had r ecen tl y become available , they had been c a rried out without ref e r ence to contemporaneous s c ientific investigations on the effect of loading duration. Furthermore, neither the en g ineerin g tests nor the load duration results offer a description of the strength o f glass; they only yield measurements of the st re ngth of different glass objects under specific loading conditions. Tha t the strength of glass has not been described, however, is only due to the fact that load duration effects have not been generalized and combined with pro babil ity theory. A complicatin g factor is t ha t of stress varia ti ons over th e glass surfaces.

The in tent of the present work .is to deve lo p and

demo nstr ate a pr a ct i cabl e formula tion for t he strength of glass. By this is meant a straightforward ma thema tical scheme that d es crib es g lass strength as a failur e probability relationship incorpor a ting the most important aspects of delayed fa ilure. While the mathematical generalization of delayed failure can be confirmed by tests from several independent sources, i t is

•

the engineering tests which permit demonstration of the

practicability of the complete formulation, for it is only in these ｩｾｳｴｳ＠ that both loading rate and glass size were varied • Nevertheless, the open literature has revealed only two

independent sets of tests that have been carried out in sufficient detaii for this purpose. (A third, limited set

of tests is also available.) The very high cost of these tests 5

Ｈｾ＠ $5 x 10 ) justifies deriving as much value as possible from them. The test results will be shown to correlate on the basis of the complete glass strength formulation, and to yield two statistical parameters ｷｨｾ｣ｨ＠ describe the strength of large

elements of commercial, soda-lime pl ate glass. Se vera l examples are worked to show applicability in design.

Although the present analysis has been limited by circumstances to consideration of plates of a specific glass material, the ge ner al formulation should be equally applicable

to objects of any particular glass material with any particular kind of surface treatment.

.

-•

THEORETICAL

Delayed failure of glass in the presence o f wat e r vapour

For pres e nt purposes, it is not nec essa ry to r eview again many important earlier investigation s on glas s behaviour. An exce l l e nt resume is g i ven by Wiederhorn (2), In order to discu ss and generalize th e implications of experimental results on d e l ayed failure, however, it is first nece ssary to hav e

available a simp l e conceptual model f or the proce ss . Muc h of this is a lready availabl e in the work of Char les (3,4) and Charles and Hilli g

(5,6). ·

Since water vapour in duc es chemi c a l corrosion in gla ss Charles (3,4) supp oses a simple rate e quation of the form,

Where : - -dz _dt i s

dz

=

Ke-y/RT dt

the ra te of progress of the glass interface perpendicular to its surface,

K is a pr e -expon entia l const a nt, R is the gas con stant ,

T is absolute temp er ature,

y is an activation energy.

•

-·

•

- 5

-By direct measurement of the rate of corrosion penetration in unstressed soda-lime glass (Corning 0800)

Charles obtains an activation energy

y

of 20±4 K cals/mol for the initial stage of corrosion.

In applying equation

(1)

to corrosion in pre-existing cracks in glass, Charles and Hillig (5,6) assume the activation energy y to be , additionally, stress-dependent and, as well, to depend on the free ･ｾ･ｲｧｹ＠ of the corrosion reaction and po s sible plastic or viscous deformation. These additional terms, of

somewhat speculative ｮ｡ｴｵｾ･＠ and magnitude, are conside r ed to be of import anc e only at low stresses where they result in a

fatigue limit stre ss below which failure will not oc c ur. Available test results, however, have been carried out in

ＮＺ ｾＺｲ｣ ＺＺＮ＠ ... ｲ｣Ｎ Ｑ ｾ ｧ･ ｳ＠ wh er e no limit is apparent; consequently , for

present purposes y will be c onsidered to be dependent on stress alone.

Ma rsh (7) , on the other hand, considers plastic-viscous flow to be of major importance in the delayed failure process. Whi le i t is not possible to reconcile this concept in mathematical det ail with Charles' and Hillig's subsequent derivations, i t can be shown, nevertheless, that identical generalizations result.

•

Making use of a mathematical solution for the st r ess di st ri bu tion about a two-dim e nsional elliptical cr a ck, Charl es and Hillig derive from eq uation (1) an expression for the ｲ｡ｴｾ＠

of

change

of

geometry of a ｰｲ･Ｍ･ ｸ ｩｳｾｾｮｧ＠

flaw.

With:

their equation (7) reduces to: d(x)

ｾ＠

dt

-Y

₀ /RT

• e •

for large x/p. Here x and p are the depth and tip curvature (2)

(3)

radiu s , respectively, of the flaw; K

1 is a constant; and om is the t e nsile . stress at the flaw tip. The form of y

1 (cr) . is unknown a prio ri, but

*

where C1 is the applied stress at the glass surface .

There are several possibilities for imperfection in equation (3). Firstly, no allowance was made for changing stress distribution as the flaw geometry changes. Secondly, the flaw width at its tip may be, or may reach the limiting spacing of the

glass molecules. Thirdly, equation (4) may not apply well for the very small dimensions and high stresses ｾｴ＠ a flaw tip.

*

This is the Inglis stress concentration relationship (8) for large x/p.

I

1

In his earlier papers Charles (3,4) had assumed empiric a lly th a t d(x) ｾ｣ｺｋ＠ • o n • dt 2 m -Yo/RT e (5)

The resulting integrated form was found to c o rrelate experiment with good precision. Almost the same result is obtain ed b y treating x/p a n d t as piece-wise separable in equation (3), thus:

•

2+n/2 (.?!.)

p

where n and

a

are constant s.

-y

/RT

• e 0 • dt (6)

ｅｸｰ･ｲｩ ｭ･ ｮｴ｡ｾｬｹＬ＠ n turns out to be large and constant

to high degree, thus, as pointed out by Charl es, t he value of (x/p)Z+n/2 at or near failure is much greater than the initial value. It follows that for a specific flaw which leads to failure,

tf n

I

J

(-

a

)

e-Yo RT d t :::: constant

o Ta

(7)

Here tf is time to failure .

In order to accommodate Marsh's plastic-viscous flow into equation (6) i t is only necessary to assert that the

I

- 8

-X

exponent on (-) remains lar ge . _p It is then immaterial wh e ther fla w g e ome try chan ge s occur as a result of changes in x or p o r both, a nd equat i on (7) applies as . before.

Ex p e r im e nt a l v e rif ic ati on

Although implied, Charles did not complete the generali z ation of equation (7). Rather, he carri e d o ut t h e inte g ration for the t wo ca se s of

a

constant, and

a

incre as in g a t const a nt rate. Charles e xperimental results f or bend i ng of

,

small rods of soda-li me glas s (Corning 0800) in sa t urated

water vapour are given in Figures 1 to 3. In Figure 1

(constant ｡Ｉｾ＠ i t is only at temperature s below about - 50°C that notic e able deviation fro m the constant n for m of

equation (7) becom es apparent. This deviation is a result of the presumably a p proximate nature of equation (6) and

X

ne e lect of the second a ry term for

p

in integration of equation (6) . Figure 2 gives measured average failure stresses at 25°C for constant rate of load application.

Figure 3 gives Charles' determination of y

=

18.8 K cal/mol

0

as obtained by setting a • o in equation (7). In developing equation (2), however, Charles and Hillig expanded y as

y •

ｹｯＫｾＩ＠

a+

••••••

0

'

This form indicates a

=

1 as a first approximation. As may be seen from Figure 3, this assump tion yields

y

=

25 K cal/ mol

0

and gives a correlation which is considerably i mproved in the high temp e rature ran g e . (Since the upper and l ow er limits of Figure 3 have been obtained by extrapolation, there appears to be no merit in attempting to obtain a more precise value for a .)

Wiederhorn (2,9) has observed the rate of p ro gress of large, artificial cracks. For relative humidities greater t han about 5 % at room te mpe ratur e and velocities

ＨｾｾＩ＠

less than about 0.01 mm/sec, his results are consistent with the forms of

equations (1) and (6) but not sufficiently ､･ｴ｡ｾｬ･､＠ to dis-tinguish between them. At higher velocities Wiederhorn's

observations indicate an effect attributable to the limitations of diffu sion of water vapour to the crack tip. At still higher velociti es, crack progress becomes independent of relative humidity. Obviously, however , high velocities will only be operative for very short ti mes in glass failure; consequ ently,

low velocity growth will ordinarily predominate overwhelmingly in equation (7).

Wiedcrho rn (9) also investi gated the effect of relative humidity on crack velocity. His theoretical development indicates velocity to be approximately proportional to relative humidity

'

raised to the power of the number of water molecules reacting with a single glass bond. Experimentally, this number appears

to be 1 for relative humidity greater than 1 to 10 %; for lower v a lu e s of RH the number appears to be 1/2. Charl e s (3) carried out one series of tests at 50% RH which yielded strengths about 7% hi g her than at saturation. This appears to be consistent

with Wiederhorn 's work indicating velocity directly proportional to RH (this would indicate strength at 50% RH to be 4.6 % higher than a t saturatlon).

Mould and Southwick (10) investigated delayed failure in constant load bending of wet, ar tific ia ll y rou g hened

microscope slides with various abrasi on s . Close inspection of their results shows that while the individual series of

tests show some irregularity there is no r ecognizable deviation from the form of equation (7) with n = 16 as found by Charles. ·.

Some const an t rate of loadin g results (constant

temperature, 296°K) by Kropschott and Mikesell (11) are given in Table I and ｣ｯｭｰｾｲ･､ ﾷ＠ with preddction by e quation (7)

Tabl e I

Loading rate Comparativ e average Predjcted

8 failur e stress (81 17)

1 psi/sec 1. 00 1. 00

10 psi/sec 1.11 1.14

On the basis of apparent general agreement with experiment a l data, equation (7) appears to be adequate to de s cribe th e delayed failure characteristics of glass in water vapour . Introducing Wiederhorn's relative humidity

effect for s oda-lime glass, in particular, the result is, again, for any specific flaw which leads to failure:

constant = S (9)

<:Vt

Here, RH is the decimal relative humidity. ' For the special situation, in particular, of cr

=

S

t,

(S

constant), for

one-o 0

di mensional tensile stresses at constant temperature T and

0

constant relative humidity RH , equation (9) ｢･｣ｯｭ･ｾ＠ ;

0 where: t

-y

/RT cr£

=

C{/

RH • e 0 • 0 n ·1

S

T

(n

+ 1)

+l

C

= {

o o }n RH e-Yo/RTo 0 dt} 1

n:rr

and cr£ is the failure stress for the condition cr =

S

0 t.

(10)

(11)

From equation (10), i t may be seen that for samples arbitrarily stressed in tension at temperature T and relativ e humidity RH (all time-dependent) for time t there corresponds a specific stress cr£ and, consequently, a specific failu r e probability P.

•

While it is clear tha t stress alo ne is not a fa ilure criterion, nevertheless, equation (10) makes it possible to retain this simple concept in the sense of a ｳｴｲ･ｳｳＭ･ｱｵｩｶ｡ｬ･ｮｾＮ＠

This concept will be u sed in most of the remaining portion of thi s paper.

Appro p ri a te mathematical statistic s f o r gla s s

As in di cated in the introduction, the initial flaw size distribution in a set of samples will generally be

arbitrary, i. e. not conforming to any of the wel l known mathe -matical distribution functions. Under the cir cumstances , it is

thus en tirely permissible to choo se a contin uo u s function which offe rs the s im ples t approximate mathemati c al description of t est result s . This is the Weibull function.

In his i mp ort an t paper, We ibull (12) pro po se s a

relationship between failure prob abili ty and stress of the for m:

. p = 1

-Ao

for samples of a given surface area, A •

I 0

experimental constants.

(12)

Here k and m are

In actual fact, surface stresses will always be two-dimensional. As shown in Appendix I, however, there exists a one-dimensional stress-equivalent at every surface location. Conseq uen tly, accepting only that glass failure is a weakest-link, surface* phenomenon, the ｰｲｯ｢｡｢ｩｾｩｴｹ＠ of failure of area

*A strength-volume effect of negli g ible magnitude is probably also pre se nt. In addition, the cut edges of glass, if in tension, experience a severe strength-line effect.

•

elements of size A

=

NA , can be writt en : 0

t

P

=

1 - exp[-k(!_) E N

a

m]

A A

l

E

0

Application to rectangular plates

(13)

For the special case of · rectangular plates,

oE

can be written:

a

a ₀ • f(x 1.. _t)

E EC a

,

i

,

(14)

whence, equation

(13)

becomes

.

.

1

A o m] PA ""

-

exp [-k(-) _A

.

I

•

_EC (15) 0 where I _""

fl

!1

[f(x

,

1.. t)) m d(x)

.

d (1..) i

,

0 0 a a i

(16)

Here, x and y are coordinates on a plate of width a and length

i,

and ｦＨｾ＠ ,

f ,

t) symbolizes

a£

varying with posi-tion and time. a is a convenient reference value for the

Ec

one-dimensional stress equivalent, usually that at the plate center.

Approximation:

Some mathematical difficulty now arises in computing I as a result of the fact that the relative stress distribution in plates ordinarily changes with chan ging pressure load.* To avoid

tThe equivalent expression for a glass edge, obtainable wi th the help of equations (10,11,12) is:

Here, o is the tensile stress on the edge of length i, and ｾ _{Ｐ＠ is}

a r eference length. In ge neral, k and m will differ from glass surface values.

*The deflections of thin glass plates usually fall in the non-linear range where both be ndin g and membrane stresses are important.

'

...

obviously unwarranted amounts of computation, however, i t is shown in Appendix II that, as an approximation, the product

..

I • crEcm in equ a tion (15) can be replaced by

. .

a ·

n m t

n

=

em [

J

0 n+l (ri) m ﾷＨｾＩ＠ T -Y /RT ]n+l • RH•e 0 _{dt (17)}

(The detailed definitions of r and

I

for equation

(17)

are giv en in Appendix I I . )

Stress distributiont

For thin, uniformly loaded, rectangular glass plates with edges free to move in their plane, elastic theory requir e s a relationship between stress cr and ｾｲ･ｳ｡ｵｲ･＠ load q of the

general, non-dimensional form: 4

=

Q[S

(2-)

E h (18)

where: cr is any specific stress at surface location Ｈｾ＠ ,

f>

E

is Young's modulus h is plate thickness

\

ｾ＠ is an edge restraint constant, defined

. dW

(M

0 is the edge bending moment and dxJ

as ｾ＠ = .!___ dH) M dx 0

0

is the slope

0

of the deflection surface at the edge. For present purposes ｾ＠ is assumed constant along all edges . )

Eh3 R..

for constant ＭＭＭｾ＠ and

a a

2

both cr(-a) d h • d I d d

•

..

4 4

only on ＡｉＮ･ｾＩ＠

.

Thus, for a limited range of !!.(a)

'

it is E h E h permissible to write: n+l 2n

4

rl m

•

(J n = En(h) B[!l(!!.) ]8 uc a

E

h 4s-2n

• B •

En - s • (:) • qs 4 Where B and s are constants for a particular range of

fC*) .

(19)

(20)

Inserting ･ｱｵ｡ｴｾｯｮ＠ (20) into equation

(17),

and equation.

(17)

into equ a tion (15) now gives:

m

PA = 1 - exp[-kC

This is a practicab le, ge n era liz e d failure probability relation-ship f o r uniformly loaded rectangular plates, incorporating effects due to pl a te ge ometry, area, load durat i on, rel ati ve humidity and temperature. The constants B and s obtain from

elastic theory or elastic tests, while k and m must be determined from failure tests.

•

:

..

COR RELATION OF TESTS ON PLATES

Av ailab le experimental data

Only the following ｲ･ｾｵｬｴｳ＠ (for commercial soda-lime glass) have been reported in such a way that they are amenable to analysis:

(1) Bowles and Sugarman (13) carried out detailed tests on 210 panels of 41" x 41" plate and sheet glass manufactured by Pilkington Bros. (U.K.) with thickness varying between 0.11 inches and 3/8 inches. The glass was uniformly

loaded and edges were supported without restraint (si mp le support). The tests were carried out at approximately constant rate of change of deflection to cause breakage

in about 30 seconds. The results are summarized in Table II.

(2) A very extensive series of proprietary tests on over 2000 lights of plate and sheet glass of various thicknesses up to 3/4" and sizes up to 10 feet by 20 feet has been c arried out by the Libbey-Owens-Ford Glass Co. (U.S.A.) (14). The test results hav e only been made public in the form of charts (Figure 4) which, however, can be compared with the Bowles and Sugarman work. These tests were also carried

I out at approximately constant rate of change of deflection:

-·

actually cent er deflection was increased in increments of

•

, .

0.1 in ches and held for 60 to 75 seconds at each value (60 seconds nomin a l plus up to 15 seconds for adjustment.

Since d eflection at failure was about 1 inch for the lar ge r plates, the total loading time was abou t 35 times greater than in the Bowles and Sugarman tests.

(3) More limited tests similar to the above on fewer, (20) lights, (Pittsburgh Plate Glass Co., U.S. A.) are r epor ted in s omewhat more detail by Orr (15). Although very

limited in number, t he results do not appear to differ greatly f rom those of Figure. 4. The principal value of Orr's work here, however, is th at it indicate s the effe ct that ed ge gla z ing may have on deflection and stresses.

Deflections in simply - su pport ed square pla t es

In order to make use of equa tion (21) in comparing the Bowles-Sugarman and L-0 -F data, it is necessar y to specify the vari a tion of q with time. In both cases the p l ates we re loaded s uch that the centre deflection was increased approxi-mately linearly with time. Since Bowles and Sugarman deter-mined the relationship between load and deflection, i t is thus

possible to establish the time variation of q •

•

•

•

..

______________

...

- 18

-Elastic theory (e.g. (16)(17)) requires a relation-ship between load and deflection of the form:

q

=

(22)

where W is the pl a te centra d e flection and v is Poisson's ratio

0

ＨｾＰＮＲＲ＠ for glass) .

w

4

In Figure 5, ho has been plotted against ｦ＼ｾＩ＠ for the

7

data of Table II, with E assumed to be 1.0 x 10 psi . Also included in the figure are the deflection measurements of

Kaiser (18) which were carried out on a steel plate (v

=

0.33) . (In plotting, Kaiser's results have been converted to equivalent glass results by taking due account of the different v values

(17).) Kaiser's experimental and theoretical values for

c

1 were apparently identical (C

1 = 0.176). For the Bowles - Sugarma n result s, however, a considerably larger range of variables was covered and retention of

c

2 in equation (22) ｩｭｰｲｯｶｾ､＠ correlation at high v al ues of W /h. The curve for W /h in Figure 5 is, (for glass):

0 . 0

4

w

w

2

w

4

q(:) • ·2.15 x 108 (h0 )(1+0.165(h0 ) -0.0007(h0 ) ) (2 3)

That the works of Kaise r and of Bowles and Sug arman agree so well is an indication that both studies were carried out with true simple support •

•

, .

•

Eva l uation of exper imental re sults

Both the L-0-F and Bowles-Suga r man te st s were such that:

C t l( b . .

q

=

3 '

to a close approxima ti on . Here

c

3 and b are constants which differ in each test series. F ro m equation

(24);

dt

-E..9._b-l

c

b

3

dq •

Substit uting

(25)

into

( 21)

and performing the integration gi ve s, (assuming T, RH , c onstant):

Here, t is the average time to failure corre spondi ng to

q,

(equation

(24)).

(24)

(25)

(26)

\

The ave ra ge pressure at failure,

q

corresp ond s to a specific , con stant failure probability for all test ser ies, t hus re-arr ang ing equation (26) f or q = q there ｲ ･ｳｵ ｬｾｳＺ＠

ms

• constant . ( 2 7)

The ･ｾｰｯｮ･ｮｴ＠ b is obtain ed by differentiation of equation (23),

I

w

2

w

4 0 0 .1+0 •. 165 (h) -0. 000 7 (h) b

-w

2

w

4

1+3x0 .165 (h 0 ) -SxO. 00'01 (h 0 ) ( 2 8)

None of the experimental studies reported temperature or relative humidity -- it is, therefore, necessary to assume room temperature (21°C) and average relative humidity (SO%) in all cases.

The light edge restraint in the L-0-F tests con s i sting of 1/ 8" x 3/8" neoprene gasketting in 1/8" x 3/4" aluminum

angles was rou ghly similar to that used by Orr (15), whe r e analysis shows it to have a considerable effect on the deflec-tions of plates thinner than about 3/8" with shortest side about 6 ft. As a result, consideration should be limited approximately to these dimensions in Figure 4, to ensure nearly simple support for comparison with the Bowles and Sugarman work. For square plates, however, there are two factors that permit larger square plates to be consid e red. These are: (1) the glazing has a smaller relative effec t on stres ses in square plates than in rectangular plates; and

(2) the larger plates of given thickness deflect so far into the large deflection range that membrane stresses (almost independent of edge restraint) form a large ｰｾ ｲ ｴｩｯｮ＠ of the

combined membrane-bending stresses. This is indicated by the four reported tests b y Orr on 82" x 82" square plates which

..

have been included with the Bowles-Sugarman data in Figure 5. (Plate thicknesses 0.237", 0.240", 0.303", 0.301".)

Table III lists the pertinent sizes of square plates for each of which 25 samples were tested by ｌｾｏＭｆＮ＠ To deter-mine W , the values of

q

were taken off Figure 4 and inserted

0

into equation (23). The average times ｴｾ＠ failure were then determined from the loading rate (i.e. about 75 seconds per 0.1 inch of deflection). Values of b were then determined from equation (28). Equation (28) was also used to determine the values of b for the Bowles and Sugarman data of Table II.

Correlation procedure

First attention will be given to the Bowles and Sugarman data since these are more thoroughly specified than those of L-0-F. In equation (27) preliminary consideration shows that s is a large number. Thus, the exponent on bt is small and since bt (Table II) does not differ greatly for all tests, a first estimate of s is obtained by plotting

q

vs h, Figure 6. Bowles and Sugarman calculated the 957. confidence range on

q,

the limits of whi c h are also shown with the data.

•

The results for sheet and plate gl a ss diff e r appre-ciably in Figure 6i apart from the fact that sheet glass appear s to be about 25 % strong e r thin plate glass, ho wever,

discussion will henceforth be confined to

t he

plate glass

results since no other s heet gl a s s d a t a is av ailable for com-parison. Accepting th e apparent slope of 1.4 for the plate glass in Figure 6, there results from equation (27):

4 -

2n/s

= 1.4, whence, with n a 16, s - 12.3.

Parameter m and coefficient of variation

The fact that Bowles and Sugarman recorded the coefficient of v a riation (v) on q and on W now permits an estimate of p a rameter m for their data. Weibull (pag e 13) gives an equation and table , Appendix III, relating the

exponent (n+l)/m(s+b) in equation (26) to the coefficient of variation on q. Although there can be little precision on determination of this coef f icient f or only 30 or 40 samples in each set, nevertheless, the apparent increase in v with

q

increasing thickness in Table!! appears to be the result of minor experimental error arising from over-lapping pressure measurements on different ｧ｡ｵｧ･ｳｾ＠ This becomes apparent when the coefficient on q is determined from that on W. Assuming negligible variation in h · (as reported by Bowles and Sugarman) this requires

v • v

/b.

,.

.

_,

way are also given in Table II, where they show considerably increased uniformity for plate glass but are inconclusive for

·-the more limited sheet glass results ·. Accepting a mean value of

v

=

21.5% for all plate glass results,Table VI (Appendix III)

q

m(s+b)

gives n+l •

5.5,

whence, m = 7.3.

The exponent on A/A in equation (27)

0 n+l thus becomes - - --ms 1 1 1 5. 3.

In Figure 7 values of

Ｍｱ ﾷ Ｈ ＭｾＩ＠

5 • 3 ( bt ) 12 ' 3 have been

A 12.3+b

h 0

plotted against (-) for both the L-0-F and Bowles-Sugarman a

data. (The reference area A has been taken to be 1.0 sq ft.)

0

Agreement between the twc sets of data is exceptional.

Implications of the correlation

The simplest way to illustrate the direct implications of Figure 7 is to compare the actual breaking pressures

q

of Table III (L-0-F) with those that would be obtained by designing from the Bowles and Sugarman data with the unreliable ad hoc assumption that failure occurs independently of load duration and plate area when the stresses are the same in both cases. For this purpose, equation (18) shows i t is only necessary to enter Figure 6 with an equivalent thickness hE

=

h(40.5/a),

(where h and a are the actual thickness and plate width in inches in the L-0-F tests). The results are summarized in

.

-Table IV where column (3) gives the indicated breakin g pr ess ure and column (4) gives the ratio of indicated to actual bre ak in g pressures. The ratio has the s ignificantly large r a nge of 1.4

to 1.9 dep e nding on the plate size , This ｭ･｡ｮｾ＠ that the s ma ller, more rapidly loaded plates of the Bowles-Sugarm an tests will

withstand loads 40 % to 90% greater than the lar ge r, slowly load ed plates of the L-0-F tests, Column (5) shows that

approximately

1/3

of the load inc rease is attributable to load duration ､ｩｦｦ･ｲ･ｮ｣･ｳｾ＠ while the remainder (between about

1/4

and

1/2,

column

(6))

is due to area differ ences . Column (7) gives

the combined calculated elfect of load duration and area . Th e values are sufficiently close to those of column (4) that

further attempts at refinement do not appear warranted at this time.

It appear s likely th at most of the residual diff e r e nce of about 15 % betwe en the two sets of data in Figure 7 is attri-butabl e to the edge glaz ing in the L-0-F tests. This being s o, then Figure 7 may fairly represent universal strength c ha r a c-teri s tics for ordinary soda-lime plate g lass, As pointed out previously, the limited tests by Orr (15) using plate glass from a third (PPG) source indicate essential agreement with the L-0-F results. It seems then that there is sufficient evidence

:

further to obtain, in addition to m, a value of k (equation

(12)): thereby, the strength characteristics of this type of

glass will be completely determined for the structural usage range. Determination of k is made possible by the investiga-tion of Kaiser ( ·\8) who measured th e two-dimensional stress distribution over the surface of a thin, square plate. With k det ermine d, any plate glass ｾｴｲｵ｣ｴｵ ｲ･＠ may subsequently be designed after determining surface stress di stribu tion either by strain measurements or from elastic theory.

failure tests are necessary.

No further

Should it turn out, on subsequent investigation, that Figure 7 is not representative of all plate glass, then the values of k ·and m her e established apply, in any event, specifically to the commercial glass tested by Bowles and Sugarman.

The proc edure for determining parameter k is given in Appendix IV. ｾｮ､＠ all parameters are summarized below:

,..

Stren g th ch a r a ct e r is tics of lar g e areas of s o da-li me p l at e g lass

Based on one-dim e nsional t e nsile tests on specimens of one s q uare foot area, at a rate of stress increase of

B

e 100 psi/second at 295°K and SO% relative

0 humidity: m = 7.3 k "" 5 X

y

/R

=

0 . m =

l

This paper 10-30 psi-7.3 } Charles (3)

Insertion of tnese values into equation (21) gives the probability of failure of a plate as dependent on the strength pa r a met ers, the plate geometry and the manner and duration of uniform pressure loading. In design, interest centers on maintaining a low value for failure probability. In this case, equation (21) simplifies to, after inserting all parameters;

(29) Equation (29) can also be re - arranged to permit an estimate of

the required glass thickness to withstand a ｧｩｾ･ｮ＠ load with a given failure probability, i.e. ·;

=

1

Yo

1 1 1 X lo- .28A 0.43 16_8 t RH .T0 16 - - ( - - - ) h = [(1.23 a PA ) B E

f (

₀ 0.5

)( )

T

e R T T0 qsdt]4s-32 (30) Here the thickness h and plate width a are in consistent units, A is the plate ·area in sq ft, q and E are in psi, and time t is in seconds. T is the absolute reference temperatur e, assumed

0

to have been 295°K in the reported tests . B and s are general parame ters dependent on edge restraint ·and plate shape.

Examples

Id eally , all design should be based on a pre-established probability of failure during the lifetime of a structure . In this section, a simple comparison will b e made of the thickn ess of glass plates with differe nt edge support which have the same failure probability under a given, arbitrary, uniform pressure loadin g of specified duration .

Other than the work of Kaiser for simply suppo rt ed squar e plates, the literature does not immediately appea r to contain stress distribution solutions, that are pertinent to the types of edge support en countered with real plates. At present, then, examples are ｾ･｣･ｳｳ｡ｲｩｬｹ＠ limited to somewhat arbitrary conditions. A simple solution is available, however, for rectangular plates s upported on two opposite sides. Since this solution approaches that of long narrow plates supported

on all sides, it will be useful for illustrative purp o ses to comp a re its thickne s s requirements 'vith those for simply supported squ a re plates .

For rectangular plates identically support e d only on two opposite sides, the surface stress distribution is as

follows: where D = 2 12(1-v ) 2 X X - 3{(-)-(-) _{a a} CJ • VCJ . y X 1

-

] 6(1+2El) a

, is the modulus of rigidity;

ｾ＠ = 0 represents fixed support and ｾ＠ • ｾ＠ represent s simple

support.

The relative tensile stresses of eq u a tion (31)

( 31)

(32)

( 33) .

occurring with simple, med ium (edge stress equa ls centre stress), and fixed support are shown in Figure 9.

Since, for plates supported on two oppos ite s ides, t he stresses ar e linearly proportional to load q, there results s a n = 16 and evaluation of B becomes a re lativ ely simple matter.

Value s of B for simple , fixed, and intermediate support ( c e ntr e stress equals edge stress) were calculated and found to be

•

A reasonable design failure probability might be 0.001, i.e. 1 in 1000. Inserting this value of PA' the several values of B, two valu es of A, a uniform pressure load of 0.20 psi and

8

two duration times of 60 se co nds and 1 x 10 seconds into equation (30) gives the results of Table V. The se particular value s of q and time can be considered to correspond only approximately to wind loading on a window and perhaps to snow loading on a skylight or to an ｡ｱｵ｡ｾｩｵｭ＠ window.

Because the examples are arbitrary, it is of more

import ance in Table V to disc u ss comparative, rather than actual thi cknesses . In extending load duration fro m 60 seconds to 108 seconds, the thickn ess requirement i s approximately doubled

(2.3 . times for support on all edges and 1 . 6 for two edge support, Changing plate area from 4 sq ft to 100 sq ft increases the ratio h/a by 54% fo r 4-edge support , but by only 26% for two - edge

support . Decre asi ng the temperature from 2l°C (68°F) to 0°C (32°F) decr eases t he thickness by 14% for 4-edge support and by 7 % for 2-ed ge support . Two other interesting features arise : (1) for 2-edge support, the required plate thic kness b e comes app ro ximately const an t provided th e edge stress is g reat er than th at a t th e

centre; and (2) since the time and area effect ar e different fo r 2- and. 4- edge supp ort, it is possible to have situations where the thickness requirements are the same in both cases •

•

-DISCUSS I ON

The correlation of Figure 7 for soda - l i me pla t e g l ass indic a t es the practicability of de sc ri bing g l ass strength by equations (10) and (13). It appea rs likely t hat s i mi l ar result s can be obt a ined fo r gl a ss of diffe r e nt composi ti ons fo r which n and y presumably differ from tho se used herein for

0 soda-lim e g la ss .

A number of further comments are in order concernin g strength and de s ign:

(1) For correlations of th e type of Figure 7, i t is worth rec alli n g that statistic al popul at i ons may be chosen at wi l l , f or example , glass from all or f rom individual manu fa cture s ources . It sho ul d als o be emphasized that

lab oratory in ves ti ga tion s on l i mi ted num bers of small

sampl es will not yield s trength r esu lts wh ich ar e applicab l e to l arge plates of p ractical size which may be 100 ti mes o r mor e lar ge r th an th e la bo rat ory samp le s .

(2) Equat ion (10) does no t consider ve ry long - t ime dela yed fail ure for which limiting stre sses would be expected . Con sequently , desi gn on the basis of equation ( 10) will ordinarily prove somewh a t conservative.

(3) It is important to a void over-refine ments to any s in gle asp ec t of g la ss strength. Thus, for exa mple, even t hough existin g experimental data is limited, i t wo uld not appear reasonable to undertake further extensive and costly

experiment a l pro g r ams while little information is available on loads an d climat e (including the possibility of surface wea thering damage and the mundane effec ts of dirt

accumulation an d periodic cleaning). In addition , residual stresses (tension and compre ssion) of seve r al hundred psi are usuall y pre se nt in large glass areas as a result of non-uniform heating and c ooling durin g man u-fac ture. On th e other hand, as indicat ed by Tab le V, surface stress variations for real situations de se rve further attention (most stress-analysis work of the past has tended to concentrate on maximum stresses, ignoring cumulative probability effects). Possibly, the

simplest me th od to obtai n th ese surface stresse s will prove to b e experi men tal (e.g. by direct measurement with strain gauges, in the manne r of Kai ser) . Since electronic computation will be involved in convertin g

the results to failure probabi l i tie s, however, i t may prove feasible to obta in entirely theoretical · solutions from elastic theo ry. For plates in p art icular, the procedures develo ped by Lev y (19) bear considera t ion: although complex they appear to offer great generality for large deflection s with any type of edge supp o rt: meanwhile, equations (2 9) and (30) should prove of .. conceptual value i n design.

\ ;

(1) Griffith, . A.A. The Phenomena of rupture and f low in solids. Phil. Tr a n s ., Royal Society of London, Seri es A, Vol. 2 21; 1921, p. 1 63 -1 98.

Griffith, A.A. The Theo r y of Rupture. Proceedings of the First International Congress of Applied Mechanics. De lft, 1924.

(2) Wiederhorn, S. M. Effects of ·environment on the fracture of glass. ｃｯｮｦｾｲ･ｮ｣･＠ on environment sensitive me ch anica l behaviour o f materials. Baltimore, Maryland, June 19 6 5 , p. 293-316.

(3) Charles, R .J. Static Fa ti gue of Glass . J. Applied Ph ysi cs, Vol. 29, No. 11, Nov ember 1958, p . 1549-1560 .

(4) Charles, R.J. Dynamic fatigue of glass . J. App lied Phys ic s, Vol. 29, No. 1 2 , December 1958, p. 1657-1662.

(5) Charles, R.J. an d ｗＮｾＮ＠ Hillig . The kinetics of glass failure b y s tr ess corr osion. Symposium sur 1a resistance mechanique du verre et le s moyens de l'ameliorer. Florence , It a l y . Sept ember 25 -2 9, 1961, p. 5 11-527.

(6) Hi l lig, W.B. and R.J. Ch arles. Su rfaces , stress-dependent surface reac ti ons, and str eng th. High strength materials, Chapter 17, Edit. V.F. Zachay. John Wi ley

&

Sons, N. Y. 19 6 5. (7) Marsh, D. M. Plastic flow and fracture of glass . Proc.

Royal Society. Se ries A, Vol . 282, No . 1388, Oc to be r 20 , 1964, p. 33-43.

(8) Inglis, C.E . Stresses in a plate du e to the presence of cr ac k s and sharp corners. Trans. Ins t i t u t i on of Naval Architects , Vol. 55, 1913 , p. 219 - 241.

(9) Wiederhorn, S.M. Influence of water vapo ur on c rac k p r opaga-tion in soda-lime gl ass. Journal o f the American Cer amic Society, Vol. 50, No . 8, August 1967, p. 407-414.

(10) Mould, R. E. and R.D. Southwick. Strength and static fati g ue of abraded glass under controlled ambi ent conditions.

American Ceramic Society Journal, Vol. 42, No. 11, p. 542-547; Vol. 42, No. 12, p. 582-592.

•

(11) Kropschott, R.H. and Mikesell, J •. Journal of Applied Physics, 28, 1957, p. 610.

(12) Weibull, W. A statistical ｴｨ･ｯｾｹ＠ of the stren g th of ma teri a ls. Ing e niorsvetenskapsakademiens Hand l ingar NR 151, Stockholm 1939, p. 1-45.

(13) Bowles, R. a nd B. Sugarman. ·The strength and deflection characteristics of lar g e rectangul a r glass panels under uniform pressure. Glass Technology , Vol . 3, No. 5, October 1962, p. 156-170.

(14) Libbey-Owens-Ford Glass Co., Toledo, Ohio, U.S.A. for Construction/1967 AlA- File No. 26-A-1967.

Glass

(15) Orr, L. Engineering properties of glass.in: Windows and Glass in the exterior of buildings. Publication No . 478, The Building Research Institute, Washington, 1957, p. 51-62. (16) Mansfield, E.H. The bending and stretching of plates.

Pergamon Press, MacMillan Co ., New York, 1964.

(17) Brown, W.G. Effect of Poisson's ratio for large deflec-tions of elastic plates. (unpublished manuscript)

(18) Kaiser, R. Rechnerische u. experimentelle Erroittlung der Durchbiegungen u. Spannungen v. quadratischen Platten bei freier Auflagerun g a. d. Randern, gleichroassi g verteilt e r Last u. grossen Ausbiegungen. Zeitschrift fur angewandte Mathematik u. Mechanik . Band 16, Heft 2, April 1936, s. 73-98.

(19) Levy, S. Bending of rectangular plates with large deflec-tions. National Advisory Committee for Aeronautics,

•

Appendix I - On e -di me n s ion a l s tr e ss equivalent of a t wo-di men s ional s tress

For principal stresses

a

, a ,

the normal stres s at

u 0 v angle X to

a

is: u

cr

_nor

=

a

_u

2

av

0

2

(cos

X

+

a

sin

X)

u

and, from equation

(12)

F ollowin g Weibull

(12),

p.

14,

a

contributes £

nor

(A-1)

(A-2)

partially to failure probability: the integrated probability is

Here, th e integration limit X is ｾ Ｏ Ｒ＠ when both

0

principal stresses are tensile, otherwise:

Now,

-1

fC1:

xo

a tan

J

Ｍｾ＠

for a one-dimensional stress

a

,

ul

(A-3 )

(A-4)

• Also, where Setting: mn /+Xo(cos2 x )n+ l dX •

In

-xo m • _{1 n+l} .mn . 2m 1 +1 r.( ·. 2 ) f(m₁+1)

and equating (A-3) and (A - 5) gives:

(A-6)

"" ( A-7) m 1 n - - -l r(ml+l) +xor;t au n 2

a

=

c [ ,- •

₂

+

₁

f

;{ (

T) ( cos

x

+

£ y 1T ml

-x

0 •

a

v

a

u 2 -y / RT }n+l m sin X) •RH•e 0 _{dt d X)}

r <

)

o . 2 (A-8)

This is the one dimensional stress-equivalent of a tw o-dimension al stress for the conditi on s of equations (10) and (1 2 ),

•

Appendix II - Approximations

In general, th e surface stresses for mos t plates wi l l n ot vary linearly with applied load, 'thus

o /o

will be time

v u

depend ent. To avoid th e co mp utation difficulties which this introduces into evaluation of equation (A-8), qu as i-lin earity

ｾｩｬｬ＠ be assumed. Thus, with

equation (A-8) becomes:

1 1 r(ml+l) +xo 2

• o

[-

•

f

(cos X u£

liT

_2m1+1

-x

0 2 ml + v sin X) dX]m 0 and;

o

m ( -£- ) 0 £C

r <

)

o 2 ml +xo 2 0

f

( cos X + u -xo

-m a

｛ﾣＨｾＬ＠

f)J

u

o

2 ml 0 v sin X) dX u 0_{vc 2 ml} + 0 sin X) dX uc

Here, subscript c signifies a reference location.

The l arge exponent n = 16 indicates weak time

-(A-9 )

(A-10)

(A -ll)

\

depend ence . Thus, instantaneous stress values could be in s erted into equation (A-ll) for determination of I by equation (16). The procedure can be improved, however, as follows:

•

•

thus, where In equation (15) set;

m

n "'

I CJ CC ·

by virtue of equations (9) and

(A-10)

t . cr. n e-Yo/RT crec m

..

n/I ""

em •

r[/ ＨｾＩ＠

•

RH • 0 · T [__! f(m1+1) +x 2 (] 2 ml

f

0

''C

r • (cos X + - - sin X)

ITT

. 2m₁ +1 -x (]

r

<

)

o uc 2

m

dt]n+1 dxJ

Now, re-insert I and r under the integral sign in

(A-14), i.e.: t n+1

n -

em{/ (ri) m 0

o

n

.

ＨｾＩ＠ T m • RH • e-Yo / RT dt} n+l (A-13) (A-14) (A-15) (A-16)

c-1

•

Appendix III - Table VI (Weibull, p. 13 - Table I)

Parameter Coefficien t : ·m(s+b) m of M

-

_j

...

fooe-z dz n+1 0 .. .V.aria t ion 1 1. 000 1. 00 2 0.886 0.52 3 0.896 0.36 4 0.908 0 . 28 8 0 . 940 0.16 16 0.965 0.09 00 1.000 0.00

•

•

•

Appendix IV - Deter mi nation of Paramet e r k

Using Weibull's d ev elopment (12) page 13, i t can readily b e shown th a t: ' .

m n+l m

1 _En-s} n+l _{, { -}A. m _(a) 4s - 2n _{.E.!_.q s}} - n+l

-

...

k Here: A 0 h s+b m(s+b) m(s+b) i f t ｻＯｾ･ｸｰ｛ Ｍ ｺ＠ n+l ]dz } n+l m 0 . 651, 0 .(A-17)

where the integrated value is obtained from Table VI for m(s+b)

n+l :z 5.5.

A value of 9.33 x 1018 for the last bracketted term rais ed to its exponent 7.3/17 in equation (A-17) is determined directly from Figure 7.

Because Kaiser measured the two-dimensional stress distribution over the plate surface, it is possible to obtain

n+l an independent value of ri (equation (17)) or of (ri) m

o

0

c

for insertion into equation (19) to obtain B: this is the last remaining unknown in equati on (A-17).

Kaiser measured both · bending and membrane

stresses at 49 locations on a steel plate surface. Mean values were then determined giving the stresses at 10 locations on a one-eighth (i . e. symmetrical) segment of the. plate •

•

•

For present purposes, the stresses were first con-verted by the method (17) to account for the difference in P o i s s on ·,· s r a t i o f o r g 1 a s s and s t e e 1 • · W i t h a v a 1 u e o f

m

1

=

6.9, equation (A-ll) was then calculated for all loca-tions. The integration indicated in equation (16) was then performed to obtain a value of I. In the case of a square plate, the factor r (equation (A-15)) is a permanent constant

since cr

uc

=

cr vc The product ' ricr

6 •9 uc n+l m

--

-=

{(ri) m cr n}n+l uc was

then computed and plotted against the corresponding value of

4

ｾＨｾＩ＠

_E

_h i _n Fi _gure 8 _• All computations were carried out electron!-cally with occasional rough checks by hand.

In the form of equation (19), Figure 8 yields B

=

-6

3.02 x 10 for the extreme 'right of the figure; this is the range correspondin g to bowles and Sugarman's tests on 1/4" and 3/8" plates. (Note: the corresponding slope in Figure 8 gives sm

n+l

=

4.8, in moderately good agreement with the earlier determin ed value of 5.3.)

Reference conditions:

Room temperature (295°K) and 50% relative humidity are suitable reference environment conditions •

•

•

•

An easily remembered st a ndard loading rate of eo

=

100 psi per second is suitab·le .

With these two conditions, the factor

m

m n+l

{RH.e-y

0

/RT}

•Cm

Tn in equ a tion ' (A-17)beco mes{S (n+l)}n+l • . . 0

m

1700n+1, from equation (10). Inserting the various constants, and withE • l07. psi, equatioh (A-17)

ｹｩ･ｬ､ｳ

Ｎ ｾ＠

k ' a

5

x l0- 30 psi- 7 • 3

plate glass sheet glass Nominal Thickness ( 1/8 in.

ｾＳＯＱ

Ｖ＠

in.

-

_{( 1/4 in.} ( Mean

TABLE II--TEST DATA BY BOWLES AND SUGARMAN ( 13) FOR 41"

x

41" GLASS PL AT ES* , UNIFORH LY LOADED

Co eff i- Mean Co eff i-Mean cient of Cent e r ci e nt of

Bursting Varia- De flee-

Varia-Thickness No. of Pre ss ure ti o n

(%)

tion ti on

( %)

(inches) Samples (p si ) ＨＱ｟Ｉｾ＠ ｟Ｈｩ｟Ａｬ｟ ｾｨ｟･＠ s ) _(_2) 0.122 40 0.754 17.3 0.760 8.6 0.197 30 1. 412 18.0 0.72 6 9 . 2 0.245 30 1. 811 2 5.0 0. 6 51 12.1 '

.

(

3/8 in. 0.373 30 3.625 23.7 0.610 14.0 ( 24 ( 32 ( (3/16 oz . oz. in. 0.110 0.158 0.195 30 30 30 0.692 1. 369 1.910 14.0 1 5.9 20.5 0.807 0.870 0.860 7.6 7.2 11.0

*

Plates were tested in a 40" x 40" ｯ ｰ･ｾｩｮｧ＠ on a rubber gasket. Thus, the effective plate size is c l o se to 40 .5" x 40.5".

c Av e r age Ti me

-to Failure _( s e cs) 35.1 3'•. 1 30.9 29 . 4 37.0 . 38.1 :37.6 bl ( eq u a -ti on 2 8) 0.4 2 0.44 0.49 0.63 0.45 0.42 0.42 b2 (2)

i l l

0.50 0 .50 0 . 47 0.58 0.56 0.45 0 .52 va I \) Ｈ ｾ Ｉ＠ b l 2 1 21 25 22 17 17 26

Plate Size

(1) 8' X 81 X 3/4"

(2) ₆1

X 61 X 1/2"

IN DEVEL OPMEN T Of FIGUR E (4)

w

ａｲ ｾ｡＠ (-.£.) _h _9.(a) 4

w

(s q . _{( e qun . 0} ｾ Ｎ＠ q(Fig.4) E h 2 4 ) (inches) 64 1.85 51 1. ·65 1. 24 36 1. 70 74 2.05 1. 02 ,-(3) 8.94' X 8.941 X 1/2" 80 0.77 165 3.05 1 . . 52 ( 4 ) 10' X 101 X 1/2"· _{100 0.62 205 3 . 40 1. 70} (5) 6 I _X 6 I _X 3/8" ₃₆ 1.17 160 3.00 1.12

-(6) 8' X 8' X 3/ 8 " 64 _{0.66 285 3.85 1. 44} (7) ₁₀1 X 10' X 3/8" _{100 0.42 445 4.75 1. 7 8}

-·

.,. b ₁ =

-

' t (equn.

｢ｴＨ｢ｾ

｢Ｉｳ＠

(s e c) _{28 ) s .} 930 0.62 580 1.36

.

I 770 0.55 420 1. 33 1140 0 . 47 540 1.3 6 1270 0.45 570 1.36 840 0.47 390 1.32 1 080 0 . 44 470 1.3 4 1340

_-

_. 0.42 560 1.36

.

'

0 .)

(2) (3)

_II

( 4 )

_II

(5) / (6)

_II

(7)

Indic ated

ｾ･｡ｮ＠ Bursting

Bur sti ng _h

_t

Pressure Lo ad ,'t

Plate Siz e Pre ssu r e e Fig. (6) Ratio Duration Area**

(L-0-F tests) psi Q_ (inc hes) _{Ｍ ｾ ｾｾｱ＠}

_{_ _}

=I-

q q Eff e c t Eff e ct (5)x{6)

1) 8' X 8' X 3/4" 1.85 0.32 2.9 1.5 1. 34 1. 3 8

LB

2) 6' X 6' X 1/2" 1. 70 0.28 2 . 4 1.4 1. 31 1. 24 1.6 3) 8.94' X 8.94' X 1/2" 0.77 0.19 1.4 1.8 1. 34 1. 44 1.9 4) 10' X 10' X 1/211 0.62 0.17 1.2 1.9 1. 34 1. 51 2.0 5) 6' X 6' X 3/8" 1.17 0.21 1.6 1.4 1. 30 1. 24 1.6 6) 8' X 8' X 3/811 0.66 0.16 1.1 1.7 1. 33 1. 38

I

1.8 7) 10' X 10' X 3/8" 0.42 0.13 0.82 1.9 1. 34 1. 51 2.0 1 · " :, J)ef :tned as: . { bt _.

ｾｾ ＲＮＳＫ｢｝ｌｏｆ＠

_{{ [12.3+b)BS} bt }12.3

**

Defined as: {ALOF

I

A _BS }5. 3

t

he

=

a

40. 5 x h, i.e. he is the equivalent thicknes s for the ｾｯｾｬ･ｳＭｓｵｧ｡ｲｭ｡ ｮ＠ tests. (a is the plat e width in inch es )

TABLE V - PLATE GLASS THICKNESSES TO WI THST AN D

..

A CONS TANT UNIFORM PRESSURE LOAD OF 0 . 2 ｾ＠

WITH FAILURE PROB ABILITY OF 1 IN 1000

:

2' X 2' plate 10' X 10' pl a te

60 sec 10 8 sec 10 8 _{sec 60 sec 10} 8 _{sec 10} 8 _sec

Duration Duration Duration Dur a tion Durati o n Duration

at 2l°C at 21°C at 0°C

' at 21°C at 21°C at 0°C

I h/a h h/a h h/a h h/a h h/a h h/a h

Type of Support xl0 3 _{(in.) xl0}3 _{(in.) x10}3 _{(in.) xlO} 3 _{(in .) x10}3 _{(in.) xlO} 3 _(in.)

Simple 3.2 0.08 7.3 0.18 6.3 0 .15 4.9 0 . 59 11.1 1. 34 9 . 7 1.15 {all edges) I Simple 7.3 .18 11.5 .28 10.7 0.25 9.3 1.11 14.6 1. 74 13.5 1. 60 ! (2 opposite edges) Medium 5.2 .12 8.2 .21 7.6 0.18 6.5 .78 10,2 J-.22 9.4 1.13 {2 opposite edges)

.

-Fixed 5.2 .12 8.2 .21 7.6 0.18 6.4 .78 10.1 1. 22 9.4 1.13 I {2 opposite edges)

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0.4

0. 6

0. 8 1. 0

1.5

2.0 2.5

RECIPROCAL OF APPLIED STRESS

;

, PSI-

1

x

10

4

FIGURE 1

EXPERi MENTA L RESULTS FROM ST ATIC

FATIGUE TESTI NG OF SODA LI ME GL A SS

RODS (COR NING 00 80) I N SATURATED

WATER VAPOR.

AFTER CHARLES (3)

...

0..

.

ｾ＠ ' V ) V)

w

0:: I -Ui LLI 0:::: ;::) _.I <{ LJ.... L..lJ <.!) <{ 0::

w

>

<(

15, 0 00

14, 000

_/ ｾ ｾ＠ 0 !

.,

13, 000

_I

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0

12, 000

1

1

Slop e

=

-

,... , . . . _

-n+1

18

11, 000

/ 0

10, 000

0. 005

0. 05

0. 5

LOADI NG RATE, INCHES/ MINUTE

Fl GURE 2

EFFECT OF CO NSTANT LO A DING RATE ON AVERAGE

FAILURE STRESS AT 25 ° C (After Charles (4))

a

.e. 1 2 7 t, - 1

z

I

..

..

w._ 0 (/')

..

<:( l.J..J cr:. <:( l.J..J 1-<( ...J 0..

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80

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5/16" 31

s··

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13/ 64

11

0. 2

0. 3

0. 4

0. 6

0. 8 l. 0

1. 4

1. 8

AVERAGE BREAKING PRES SURE, PSI

FIGURE 4

ST RENGTH CHART (LIBBEY- OWENS- FORD GLASS CO . (1 4))

(Note : Ma nufacture Tolerances as Indic ated in (14) Have

E

.. 0 · ﾷ ｾ＠

-•

- V> 0... X 0 0 0 II

0

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6

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=

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70

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d.

=

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=

18. 8

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ｾ Ｚ ｇ＠

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E R A T U R E D E P EN D EN C E 0 F T H E D E LA Y E D FA 1 L U R E P R 0 C E S S

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b

0

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c

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_LEGEND

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Bowles - Sugarman (Plate)

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Bowles- S u g a r m a n ·( S h e e t )

0

0 r r

(Plate)

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_{Kaiser (Steel, Converted)}

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1

2

3

4

6

8

10

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